Problem: Let $m=2x+3$. Which equation is equivalent to $(2x+3)^2-14x-21=-6$ in terms of $m$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $m^2+7m+6=0$ (Choice B) B $m^2-7m-15=0$ (Choice C) C $m^2-7m+6=0$ (Choice D) D $m^2+7m-15=0$
Solution: We are asked to rewrite the equation in terms of $m$, where ${m}={2x+3}$. In order to do this, we need to find all of the places where the expression ${2x+3}$ shows up in the equation, and then substitute ${m}$ wherever we see them! For instance, note that $-14x-21=-7({2x+3})$. This means that we can rewrite the equation as: $(2x+3)^2-14x-21=-6$ $({2x+3})^2-7({2x+3})=-6$ [What if I don't see this factorization?] Now we can substitute ${m}={2x+3}$ : $({m})^2-7({m})=-6$ Finally, let's manipulate this expression so that it shares the same form as the answer choices: ${m}^2-7{m}+6=0$ In conclusion, $m^2-7m+6=0$ is equivalent to the given equation when $m=2x+3$.